Hall--Littlewood expansions of chromatic quasisymmetric polynomials using linked rook placements

2025/06/29 by Jang Soo Kim, Kim, Jang Soo, Seung‐Jin Lee +3 · 1 citation
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05A15 #Quasicrystal Structures and Properties #Secondary: 05A30

paper · pdf · doi:10.48550/arxiv.2506.23082

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we obtain a Hall--Littlewood expansion of the chromatic quasisymmetric function arising from a natural unit interval order and describe the coefficients in terms of linked rook placements. Applying the Carlsson--Mellit relation between chromatic quasisymmetric functions and unicellular LLT polynomials, we also obtain a combinatorial description for the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall--Littlewood polynomials.

Citations

• On Macdonald expansions of q-chromatic symmetric functions and the Stanley-Stembridge Conjecture
• α-chromatic symmetric functions
• Chromatic symmetric functions from the modular law
• A proof of the shuffle conjecture
• A modular relation for the chromatic symmetric functions of (3+1)-free\n posets
• A Combinatorial Formula for the Character of the Diagonal Coinvariants
• q-Rook polynomials and matrices over finite fields
• Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties

Cited by

• A tableaux formula for q-rook numbers

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